Ex 9.1 Q3 - A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Solution:- AC and PR are the slides for younger and elder children respectively.
Case (i): For younger children
Given,
Height of the slide = AB = 1.5 m
Slide's angle with ground = ∠ACB = 30°
➙ In ∆ABC, ∠ABC = 90°,
∴ sinC =
Opposite side of ∠C
/
Hypotenuse
∴ sin30° =
AB
/
AC
∴ sin30° =
1.5
/
AC
{ Given } ∴
1
/
2
=
1.5
/
AC
{ ∵ sin30° = 1/2 } ∴ AC = 1.5 × 2
∴ AC = 3
Therefore, the length of the slide for younger children should be 3 m.
Case (ii): For elder children
Given,
Height of the slide = PQ = 3 m
Slide's angle with ground = ∠PRQ = 60°
➙ In ∆PQR, ∠PQR = 90°,
∴ sinR =
Opposite side of ∠R
/
Hypotenuse
∴ sin60° =
PQ
/
PR
∴ sin60° =
3
/
PR
{ Given } ∴
√3
/
2
=
3
/
PR
{ ∵ sin60° = √3/2 } ∴ PR =
3 × 2
/
√3
*Multiplying Numerator and Denominator by √3
∴ PR =
3 × 2
/
√3
×
√3
/
√3
∴ PR =
3 × 2 × √3
/
3
∴ PR = 2√3
Therefore, the length of the slide for elder children should be 2√3 m.
Hence,
The length of the slide in each case should be 3 m and 2√3 m respectively.
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Try This..
✒ A man is standing 40 m away from a tower. The angle of elevation of the top of the tower from his eye is 30°. Find the height of the tower.
✒ A balloon is flying at a height of 20 m. If the angle of elevation from a point on the ground is 45°, how far is the balloon from that point?
✒ A ladder is leaning against a wall making an angle of 60° with the ground. If the foot of the ladder is 2.5 m from the wall, find the length of the ladder.
❌ Common Mistakes
Confusing the angle with the side:▸ Remember, the angle is always between the ground and the slide.Using the wrong trigonometric ratio:▸ Since height and hypotenuse are involved, always use sin(θ).Rounding too early:▸ Keep at least 3 decimal places in intermediate steps to get accurate answers.Forgetting the unit:▸ Always include meters (m) in your final answer.
📝 Related Questions:-
- Ex 9.1 Q1 - A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.
- Ex 9.1 Q2 - A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
- Ex 9.1 Q4 - The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
- Ex 9.1 Q5 - A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
- Ex 9.1 Q7 - From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
- Ex 9.1 Q8 - A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Queries Solved:-
Class 10 Ex 9.1
Ex 9.1 Q3 Class 10
Class 10 Ex 9.1 Q3
Class 10 Chap 9 Ex 9.1 Q3
Class 10 Some Applications Of Trigonometry
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